I will first present vectorial total variation minimization methods combined with the log barrier for denoising high angular resolution diffusion images (HARDI) of the brain. HARDI data is a powerful new extension of diffusion imaging, which goes beyond the diffusion tensor imaging model: mathematically, intensity data is given at every voxel and at any direction on the sphere. Since HARDI data is usually contaminated by noise, we present a minimization model for denoising that takes into account the data formation model. Theoretical and experimental results will be presented. This is joint work with Yunho Kim, Paul Thompson, Liang Zhan and Arthur Toga.
If time permits, I will also present mouse atlas to gene data registration methods in the presence of nonlinear elasticity smoother and landmarks. A particular numerical method that removes the non-linearity in the derivatives will be introduced. Combined with Sobolev gradient implementation of the Euler-Lagrange equation, faster and improved registration results are obtained for smooth and large deformations. This is joint work with Tungyou Lin.
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